
John von Neumann (1903-1957) was unquestionably one of the most brilliant scientists of the twentieth century. He made major contributions to quantum mechanics and mathematical physics and in 1943 began a new and all-too-short career in computer science. William Aspray provides the first broad and detailed account of von Neumann's many different contributions to computing. These, Aspray reveals, extended far beyond his well-known work in the design and construction of computer systems to include important scientific applications, the revival of numerical analysis, and the creation of a theory of computing. Aspray points out that from the beginning von Neumann took a wider and more theoretical view than other computer pioneers. In the now famous EDVAC report of 1945, von Neumann clearly stated the idea of a stored program that resides in the computer's memory along with the data it was to operate on. This stored program computer was described in terms of idealized neurons, highlighting the analogy between the digital computer and the human brain.
Aspray, William (1990) John von Neumann and the origins of modern computing. MIT Press. (http://www.amazon.com/Neumann-Origins-Modern-Computing-Histo...)
Most biographies of him strangely enough don't really go into too much detail on his work at the AEC, perhaps because there's already so much to talk about but also perhaps because a lot of this stuff was classified. It doesn't help either that the earliest biographies were only written more than 20 years after he died, and back in his lifetime in the first half of the 20th century not as much was written down as these days. I am assuming you are talking about his life in the 1940s and 1950s when you say "this portion of his life" so I'll give recommendations based off that. All the main biographies generally cover it but I'll give a few notes to help you make a decision. Not in any particular order.
- The Martian's Daughter: A Memoir
His daughter's autobiography, first part of the book talks about their relationship and given she was born in 1935 most of it covers the last parts of his life.
- John von Neumann and Norbert Wiener: From Mathematics to the Technologies of Life and Death
This is the first biography by Heims; goes more into detail about their war work but I would point out though that Heims pretty clearly aims to denigrate von Neumann as a war hawk, none of the quotes are false or anything like that but when the book first came out several of von Neumann's colleagues criticized the book for trying to character assassinate him.
- The Computer from Pascal to von Neumann
Goldstine talks about the history of the computer but about two-thirds of the book covers work von Neumann and him both did together and there is plenty of biographical material on von Neumann. Obviously more focused on computers though.
- John von Neumann and the Origins of Modern Computing
Unlike Goldstine's book this is a biography von Neumann, however unlike Goldstine Aspray didn't know von Neumann as a close collaborator. Like Goldstine's it also focuses more on computing, not as much Goldstine however a lot of von Neumann's automata work is tied up with computers so it's a good read regardless.
- Prisoner's Dilemma: John Von Neumann, Game Theory, and the Puzzle of the Bomb
This book focuses more on game theory with less biographical material on von Neumann, however it does have a dedicated chapter to his last years and what he was doing then.
- John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More
This is probably the biggest biography, it is very even describing each stage of von Neumann's life. It is a bit more of a hero worship compared the other books which you'll notice if read the reviews of the book. Less technical compared to the others too.
- The World as a Mathematical Game: John Von Neumann and Twentieth Century Science
This one tries to evaluate von Neumann's contributions to 20th century science overall, as it was written in 2009 it does source to the previous books quite a bit. Shorter compared to the others.
- The Man from the Future: The Visionary Life of John von Neumann
This one was only released this year, it's a biography but it kind of tries to describe the world around von Neumann at his time and how he fits into it. Obviously by now almost everyone who knew him personally aside from his daughter and a handful of others are dead so it focuses more on his technical contributions rather than anecdotes on his influence.
- Turing's Cathedral: the Origins of the Digital Universe
This one is also more focused on computing, has some things that aren't written in the others as Dyson did a particularly good job going through some of the archives, but not as much focused on von Neumann compared to the others.
- A Fiery Peace in a Cold War: Bernard Schriever and the Ultimate Weapon
Isn't a biography of von Neumann but of Schriever, who worked with von Neumann to setup the first ICBM programs in the USA. Obviously the main focus here is on the military and political side of von Neumann's work in the 1940s and 50s, and not much else in terms of his life. However contains lots of information on this particular part of his life that other books lack.
If you look at the "Further Reading" section of his Wikipedia page there is a long list of books that feature him heavily in case you want more. Happy reading!